I don't speak Italian so could not watch the video with confidence
as to what the message is. I don't know what he is saying
nor can read the out of focus chalk marks.
I translate the words of the professor: "Let us consider the wheel as
made of separate particles moving in a circle around the axis and fix
our attention on one of them. For example this particular particle. Its
mass is m1, the distance from the axis is r1. It moves in this way with
velocity v1, perpendicular to the radius vector. We write its angular
momentum. The angular momentum is L1 equal to the momentum m1, v1
transverse by r1 (L1=(m1* v1)*r1).
We have calculated the angular momentum of the particle. We could do
the same for this, or this, or this, and so for any particle of the
wheel. And, having done this, the total angular impulse of the wheel is
found by adding together all these different angular impulses".
But your simulation animation seems to confirm exactly why it
preccesses and which direction it must take, rather than rule it out.
To start with when the wheel rotates freely your two particles
take very different path lengths. From your animation I measured
E as being 17.5 cm And Z as being 25.5 cm. (And incidentally
E&Z both only take 1 path each . Not multiple paths!)
The reason for the precession seems simple. Let's study the 1/4 rotation
paths of each particle as E moves from 3:00 to 6:00 and Z moves
from 9:00 to 12:00
E starts off moving downwards. It has gravitational pull G added to
rotational momentum R.
So it speeds up.
Z on the other hand starts off moving upwards. It also
has gravitational pull G and rotational momentum R. But although R
is the same for both Z and E,..G on the other hand is opposite to
the direction of each. In the sense that G pulls on Z reducing its speed
whilst G pulls on E increasing its speed.
To compensate for these different velocities of E and Z ....Z travels
less distance because it has a slower velocity. And E travels a
greater distance as it has a greater velocity. To compensate
without distorting its shape the wheel preccesses.
As your animation confirms.
You too make the same mistake as the teacher in the video: consider
only the rotation of the wheel on its axis.
I have updated my animation
adding a side view where there is another rotation highlighted with red
It is clearly seen that the wheel, descending by gravity, is forced to
incline following the red circumference line whose radius is the arm
This inclination is the cause of the precession and, in fact, if the
wheel did not incline, it would descend in perfect vertical, without
going either to the right or to the left.
Obviously, it depends on the principle of conservation of angular
momentum, as in the case of the ice skater who rotates faster when
bringing her arms towards her body and slower when moving them away.
In my animation, the upper half of the wheel (moving away from the axis
of rotation) slows its rotation to the right (like the skater spreading
her arms) and the lower half (moving towards the axis of rotation) it
accelerates its rotational motion to the left like the skater narrowing
As a result, the wheel moves to the left.
If the rotation is counterclockwise, the reverse occurs and the
precession goes to the right.
All of this can be used to establish an alternative method to the
right-hand rule: the direction of precession always goes to the same
side as the particles at the bottom of the wheel.
In the clockwise spinning wheel, its bottom particles go to the left
and the precession also goes to the left, in the counterclockwise one,
for the same reason, the precession goes to the right.